Classical and quantum mechanics of a particle on a rotating loop

Details Classical and quantum mechanics of a particle on a rotating loop Classical and quantum mechanics of a particle on a rotating loop

1999-04-26

arxiv.org/abs/quant-ph/9904083v1

Am.J.Phys. 68 (2000) 1128-1133

Physics

Quantum Physics

30 pages, RevTex, 7 figures

Scientific paper

10.1119/1.1286427

The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics from both exact and semi--classical standpoints. Exact solutions of the Schrodinger equation are obtained in some cases by diverse methods. Instantons, bounces are constructed and semi-classical, leading order tunneling amplitudes/decay rates are written down. We also investigate qualitatively the nature of small oscillations about the kink/bounce solutions. Finally, the connections of these toy examples with field theoretic and statistical mechanical models of relevance are pointed out.

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